questions 17 18 19 20 Let theta be in standard position, with terminal side in t

Question

questions 17 18 19 20

Let theta be in standard position, with terminal side in the specified quadrant and satisfying the given condition. Find the values of the trigonometric functions of theta . III; parallel to the line 2y - 7x + 2 = 0 IV; perpendicular to the line through A(5, 12) and B(-3, -3) If theta is an acute angle, use fundamental identities to write the first expression in terms of the second. cot theta , sin theta sec theta , sin theta tan theta, cos theta csc theta , cos theta tan theta , sec theta sin theta, sec theta cot theta , csc theta cos theta , cot theta Refer to Example 1. Make the indicated trigonometric substitution and use fundamental identities to obtain a simplified trigonometric expression that contains no radicals. x = 4 sin theta for - pi / 2 theta pi / 2

Explanation / Answer

17. a) cot@ = sqrt( 1- sin^2@)/sin@ 17. b) sec@ = 1/cos@ = 1/sqrt( 1-sin^2@) 18. a) tan@ = sin@/cos@ = sqrt(1-cos^2@)/cos@ 18. b) cosec@= 1/sin@ = 1/sqrt(1-cos^2@) 19. a) 1+ tan^2@ = sec^2@ => tan@ = sqrt(sec^2@ -1) 19. b) sin@ =sqrt(sec^2@-1)/sec@ 20. a) cot^2@ + 1 = cosec^2@ => cot@ = sqrt(1-cosec^2@) 20. b) cos@ = sqrt(1-cosec^2@)/cosec@

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